# FOM: Alice, Carol and Leibniz

wiman lucas raymond lrwiman at ilstu.edu
Wed Apr 17 01:31:35 EDT 2002

```Hi,

Miguel A. Lerma wrote:

> A linear superposition of two wave functions does not
> represent the state of two particles, but a combination
> of two states of the same particle - which is by itself
> another state of that particle

Yes, you are quite right.  I've just been learning this sort of stuff
recently (and hence my confusion).  After having done a quick review:

An "observable" (e.g. a particle) is an *operator* on a Hilbert space,
and a given "state" is an eigenvector of the operator.  A superposition
of states is a linear combination of eigenvectors, which is normalized.

In any case, if we have our two electrons, and we observe them in two
different states, then they are (for our observation) different.  When
we are not making an observation, then the question of identity doesn't
seem to have any meaning.  Furthermore, there is always a small
possibility (if I understand things right) that particles can pop in and
out of existance.  Thus at the quantum scale, counting the number of
particles may be a losing game.

To avoid the difficulties faced by a quantum world, say we have two
marbles which look identical.  If we only look at one at a time, then we
are unable to tell them apart.  Yet when we look at both at the same
time, they are certainly distinct marbles, as they will be in different
places.  Now say we put them in a bag, and shake the bag up.  Then we
will be unable to tell which was which before we shook the bag, but we
will still be able to tell them apart (there will  be a predicate which
holds for one, but not for the other).

That's the point I was trying to make:  his example of two qualitatively
identical things doesn't hold water.

- Lucas Wiman

```